Theorem equncomi 3305

Description: Inference form of equncom 3304. (Contributed by Alan Sare, 18-Feb-2012.)

Hypothesis

Ref	Expression
equncomi.1	|- A = ( B u. C )

Assertion

Ref	Expression
equncomi	|- A = ( C u. B )

Proof of Theorem equncomi

Step	Hyp	Ref	Expression
1		equncomi.1	. 2 |- A = ( B u. C )
2		equncom 3304	. 2 |- ( A = ( B u. C ) <-> A = ( C u. B ) )
3	1, 2	mpbi 145	1 |- A = ( C u. B )

Syntax hints:   = wceq 1364   u. cun 3151

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157

This theorem is referenced by:  disjssun  3510  difprsn1  3757  unidmrn  5198  phplem1  6908  djucomen  7276